Neighboring effect in Metamaterials: Wave Propagation, Energy Absorption, and Deployability

The mechanical response of metamaterials is often determined by their undeformed geometry, which restricts adaptability in dynamic environments. In this work, we explore a paradigm based on the neighboring effect, whereby the mechanical stability of each unit cell is contingent upon the mechanical state of its neighbors. This behavior arises from strong nonlinear interactions between coupled structural elements, namely von Mises trusses. Through a combination of experiments, FEM, and analytical modeling, we elucidate the underlying mechanisms of the neighboring effect and extend this principle across 1D, 2D, and 3D systems. In the 1D case, we harness spatial heterogeneities in geometry and mass to control transition wave propagation, enabling tunable dynamic responses. In the 2D, we demonstrate reprogrammable energy absorption by modulating the topological state of the lattice. Extending to 3D, we develop metamaterials composed of kirigami-inspired von Mises truss units, resulting in structures that are stable only in their fully closed or fully deployed states. These lattices exhibit complex shape transformations triggered by minimal, localized actuation, offering a scalable route to deployable systems. This work advances the frontier of smart structural systems by demonstrating how conditional stability can enable adaptive functionalities in mechanical metamaterials for applications in impact mitigation, soft robotics, and reconfigurable structures.